Articles | Volume 16, issue 2
https://doi.org/10.5194/ms-16-417-2025
https://doi.org/10.5194/ms-16-417-2025
Research article
 | 
08 Sep 2025
Research article |  | 08 Sep 2025

Study on the stability of analytical periodic solutions of nonlinear gear systems

Bing Dai, Zengcheng Wang, Zongxu Dai, Yang Liu, Shiyuan Qi, and Tao Chen

Cited articles

Al-shyyab, A. and Kahraman, A.: Non-Linear Dynamic Analysis of a Multi-Mesh Gear Train Using Multi-Term Harmonic Balance Method: Period-One Motions, J. Sound Vib., 284, 151–172, https://doi.org/10.1016/j.jsv.2004.06.010, 2005. 
Blankenship, G. W. and Kahraman, A.: Steady State Forced Response of a Mechanical Oscillator with Combined Parametric Excitation and Clearance Type Non-Linearity, J. Sound Vib., 185, 743–765, https://doi.org/10.1006/jsvi.1995.0416, 1995. 
Farshidianfar, A. and Saghafi, A.: Bifurcation and Chaos Prediction in Nonlinear Gear Systems, SHOCK Vib., 2014, 1–8, https://doi.org/10.1155/2014/809739, 2014. 
Hu, X., Liu, X., Zhang, D., Zhou, B., Shen, Y., and Zhou, Y.: An Improved Time-Varying Mesh Stiffness Calculation Method and Dynamic Characteristic Analysis for Helical Gears under Variable Torque Conditions, Adv. Mech., 15, 413–429, https://doi.org/10.1177/16878132231203132, 2023. 
Huang, J. and Fu, X.: Stability and chaos for an adjustable excited oscillator with system switch, Commun. Nonlinear Sci., 77, 108–125, 2019. 
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Short summary
The gear system with backlash is a strongly nonlinear system, and the widely used harmonic balance method cannot meet the requirements. Additionally, the quasi-periodic and unstable periodic motion analytical solutions may be derived, and the principle of chaos generation can be further explained. Therefore, the effect of the generalized harmonic balance method DTE (dynamic transmission error) on system bifurcation and stability is studied.
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